{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T15:34:52Z","timestamp":1726760092419},"reference-count":25,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[2015,5,1]],"date-time":"2015-05-01T00:00:00Z","timestamp":1430438400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"funder":[{"name":"Niels Henrik Abel Board"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2015,5]]},"DOI":"10.1016\/j.cnsns.2014.09.016","type":"journal-article","created":{"date-parts":[[2014,9,28]],"date-time":"2014-09-28T21:09:18Z","timestamp":1411938558000},"page":"1243-1251","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":31,"title":["Enhanced group classification of Gardner equations with time-dependent coefficients"],"prefix":"10.1016","volume":"22","author":[{"given":"Olena","family":"Vaneeva","sequence":"first","affiliation":[]},{"given":"Oksana","family":"Kuriksha","sequence":"additional","affiliation":[]},{"given":"Christodoulos","family":"Sophocleous","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.cnsns.2014.09.016_b0005","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1023\/A:1012667617936","article-title":"The structure of Lie algebras and the classification problem for partial differential equations","volume":"69","author":"Basarab-Horwath","year":"2001","journal-title":"Acta Appl Math"},{"key":"10.1016\/j.cnsns.2014.09.016_b0010","doi-asserted-by":"crossref","first-page":"123515","DOI":"10.1063\/1.4765296","article-title":"Complete group classification of a class of nonlinear wave equations","volume":"53","author":"Bihlo","year":"2012","journal-title":"J Math Phys"},{"key":"10.1016\/j.cnsns.2014.09.016_b0015","series-title":"Symmetry and integration methods for differential equations","author":"Bluman","year":"2002"},{"key":"10.1016\/j.cnsns.2014.09.016_b0020","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.cpc.2006.08.001","article-title":"GeM software package for computation of symmetries and conservation laws of differential equations","volume":"176","author":"Cheviakov","year":"2007","journal-title":"Comput Phys Commun"},{"key":"10.1016\/j.cnsns.2014.09.016_b0025","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.jde.2004.07.026","article-title":"Symmetry group methods for fundamental solutions","volume":"207","author":"Craddock","year":"2004","journal-title":"J Diff Equ"},{"key":"10.1016\/j.cnsns.2014.09.016_b0030","series-title":"Symmetries of equations of quantum mechanics","author":"Fushchich","year":"1994"},{"key":"10.1016\/j.cnsns.2014.09.016_b0035","unstructured":"Ivanova NM, Popovych RO, Sophocleous C. Conservation laws of variable coefficient diffusion\u2013convection equations, In: Ibragimov NH et al. editor. Proc. of tenth international conference in modern group analysis (Larnaca, Cyprus, 2004), 2005, Nicosia. p. 107\u201313. [arXiv:math-ph\/0505015]."},{"key":"10.1016\/j.cnsns.2014.09.016_b0040","unstructured":"Ivanova NM, Popovych RO, Sophocleous C. Group analysis of variable coefficient diffusion\u2013convection equations. II. Contractions and exact solutions. arXiv:0710.3049."},{"key":"10.1016\/j.cnsns.2014.09.016_b0045","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/0375-9601(91)90500-8","article-title":"On point transformations of a generalised Burgers equation","volume":"155","author":"Kingston","year":"1991","journal-title":"Phys Lett A"},{"key":"10.1016\/j.cnsns.2014.09.016_b0050","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1088\/0305-4470\/31\/6\/010","article-title":"On form-preserving point transformations of partial differential equations","volume":"31","author":"Kingston","year":"1998","journal-title":"J Phys A Math Gen"},{"key":"10.1016\/j.cnsns.2014.09.016_b0055","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1016\/0021-8928(94)90138-4","article-title":"Group classification of the equations of two-dimensional motions of a gas","volume":"58","author":"Meleshko","year":"1994","journal-title":"J Appl Math Mech"},{"issue":"1","key":"10.1016\/j.cnsns.2014.09.016_b0060","doi-asserted-by":"crossref","first-page":"170","DOI":"10.2991\/jnmp.1996.3.1-2.19","article-title":"Generalization of the equivalence transformations","volume":"3","author":"Meleshko","year":"1996","journal-title":"Nonlinear Math Phys"},{"key":"10.1016\/j.cnsns.2014.09.016_b0065","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1016\/j.cnsns.2011.09.002","article-title":"Symmetry classification of the Gardner equation with time-dependent coefficients arising in stratified fluids","volume":"15","author":"Molati","year":"2012","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2014.09.016_b0070","unstructured":"Noether E, Invariante Variationsprobleme, Nachr. K\u00f6nig. Gesell. Wissen. G\u00f6ttingen, Math-Phys Klasse (1918), p. 235\u201357; English translation in Transport Theory and Statistical Physics, 1, no. 3, 1971, p. 183\u2013207."},{"key":"10.1016\/j.cnsns.2014.09.016_b0075","series-title":"Applications of Lie groups to differential equations","author":"Olver","year":"1986"},{"key":"10.1016\/j.cnsns.2014.09.016_b0080","series-title":"Group analysis of differential equations","author":"Ovsiannikov","year":"1982"},{"key":"10.1016\/j.cnsns.2014.09.016_b0085","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/0021-8928(94)90137-6","article-title":"The podmodeli program. Gas dynamics","volume":"58","author":"Ovsyannikov","year":"1994","journal-title":"J Appl Math Mech"},{"key":"10.1016\/j.cnsns.2014.09.016_b0090","doi-asserted-by":"crossref","first-page":"073102","DOI":"10.1063\/1.4734344","article-title":"Symmetry preserving parameterization schemes","volume":"53","author":"Popovych","year":"2012","journal-title":"J Math Phys"},{"key":"10.1016\/j.cnsns.2014.09.016_b0095","doi-asserted-by":"crossref","first-page":"7547","DOI":"10.1088\/0305-4470\/37\/30\/011","article-title":"New results on group classification of nonlinear diffusion\u2013convection equations","volume":"37","author":"Popovych","year":"2004","journal-title":"J Phys A Math Gen"},{"key":"10.1016\/j.cnsns.2014.09.016_b0100","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s10440-008-9321-4","article-title":"Admissible transformations and normalized classes of nonlinear Schr\u00f6dinger equations","volume":"109","author":"Popovych","year":"2010","journal-title":"Acta Appl Math"},{"key":"10.1016\/j.cnsns.2014.09.016_b0105","doi-asserted-by":"crossref","first-page":"3887","DOI":"10.1016\/j.cnsns.2010.01.037","article-title":"More common errors in finding exact solutions of nonlinear differential equations: part I","volume":"15","author":"Popovych","year":"2010","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2014.09.016_b0110","doi-asserted-by":"crossref","first-page":"3074","DOI":"10.1016\/j.cnsns.2014.01.009","article-title":"Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries","volume":"19","author":"Vaneeva","year":"2014","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2014.09.016_b0115","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10440-008-9280-9","article-title":"Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source","volume":"106","author":"Vaneeva","year":"2009","journal-title":"Acta Appl Math"},{"key":"10.1016\/j.cnsns.2014.09.016_b0120","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.jmaa.2012.05.084","article-title":"Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities","volume":"396","author":"Vaneeva","year":"2012","journal-title":"J Math Anal Appl"},{"key":"10.1016\/j.cnsns.2014.09.016_b0125","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/0375-9601(92)90199-V","article-title":"Allowed transformations and symmetry classes of variable coefficient Korteweg\u2013de Vries equations","volume":"167","author":"Winternitz","year":"1992","journal-title":"Phys Lett A"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570414004602?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570414004602?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,9,29]],"date-time":"2018-09-29T01:58:05Z","timestamp":1538186285000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570414004602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5]]},"references-count":25,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2015,5]]}},"alternative-id":["S1007570414004602"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2014.09.016","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2015,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Enhanced group classification of Gardner equations with time-dependent coefficients","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2014.09.016","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2014 Elsevier B.V. All rights reserved.","name":"copyright","label":"Copyright"}]}}